In a large mixing bowl, whisk together coconut milk, milk, heavy cream, sweetened condensed milk, and light corn syrup. Once combined, stir in 2 tablespoons coconut flakes (not all).
Fill the popsicle molds with mixture by leaving 1/8-inch space on top. Add the remaining coconut flakes into each mold over the mixture. If using molds that contain sticks, put on lid, sticks and freeze. If using small cups, freeze until beginning to set, about 45 minutes, then insert wooden sticks and put back in freezer.
Freeze for at least 8 hours. If the popsicles are stuck in the molds, dip the molds in warm water for 10 seconds or so. Remove popsicles and serve. If not serving right away, place the popsicles on a large plate or small baking sheet that is covered with a wax paper. Cover the popsicles with another wax paper. Put back in the freezer to refreeze for a couple more hours.
Notes
Use good coconut milk for best flavor. My go-to brand is Aroy-D. It's creamy and it has a strong coconut flavor.
For storage: Place a wax paper around the popsicle and put in a Ziploc bag. They can be kept for at least 2 weeks in the freezer.
Light corn syrup gives the popsicles a dense and chewy texture, which is very important. If you switch it out to sugar, the texture of the popsicles would be much harder and hard to bite into.
I don’t like coconut flakes too much, so I only added a little bit for texture. Feel free to add more if you like them.